Is fulfilling this statement (which is found in the writings of the Prophet Micha) enough to make you into a good Jew? Yes and no. Let me give you an analogy:
Let's say NASA were to offer a twenty-year program teaching people how to design space ships that will be able to bring people to and from distant galaxies. On the first day of class the professor gets up and says to the class, "We have only one demand of our graduates, and everything you learn here over the next twenty years is based on this very simple idea: 'Bring ‘em back alive.'" Can the students now graduate, knowing this phrase? Or do they need to learn all the detailed specifications required to build a ship that will 'bring 'em back alive?'
The Talmud explains that Micha was offering an underlying principle to aid in the performance of the 613 commandments of the Torah. "Doing justice and loving kindness" are the underlying goals of all the commandments concerning the way you treat other people, while "walking privately with God" is the underlying goal of all the commandments concerning your relationship with God.
Micha is addressing people who seemed so caught up in performing the sacrifices at the Temple that they had forgotten the essence of Judaism. They did not pursue justice, love kindness and walk humbly with God as much as they should have. Micha is telling the Jewish people not to lose sight of the goals of the commandments.
So it's a mistake to think that Micha advocated non-observance of the mitzvot, or meant to minimize their importance in any way. Micha himself observed the Shabbat, ate kosher food, and kept the rest of the Torah and Rabbinic laws. He urged the people to remember Moses, Aharon and Miriam as the leaders who taught them the Torah, and he prophesied about the day when the Temple will be rebuilt and "Torah will go forth from Zion."
Hillel did the same thing when he was asked to sum up the entire Torah while 'standing on one foot.' He said, "Whatever you don't like, don't do to others. The rest of the Torah is the explanation of this statement. Go study it."
Was Hillel condoning non-observance of the commandments? Hillel himself was a Torah observant Jew, and the Talmud is replete with his halachic teachings, including laws about Temple sacrifice and the prohibition of work on Shabbat and festivals. Rather, Hillel was offering a principle which serves as a guiding focus for the observance of all the commandments.
In short, one can't be a "good Jew" with only law and rituals and no ethical dimension. But by the same token, the ethical dimension can't be accessed without the Torah guidelines found in Jewish law. Micha was talking to people who were all actions and no thought; nowadays many people are all thought and no action. We need both to be good Jews.
